2-3 Conditionals

1. 2-3 Conditionals

2. Statements • Conditional statement • A statement that can be written in if-then form • If-Then statement • If p, then q • “p” and “q” are statements • “p” is the hypothesis • “q” is the conclusion

3. hypothesis conclusion Example Identify the hypothesis and conclusion of the following statement. If a polygon has 6 sides, then it is a hexagon. If a polygon has 6 sides, then it is a hexagon. Answer: Hypothesis: A polygon has 6 sides.Conclusion: It is a hexagon.

4. Example Which of the choices correctly identifies the hypothesis and conclusion of the given conditional?If you are a baby, then you will cry. A. Hypothesis: You will cry.Conclusion: You are a baby. B. Hypothesis: You are a baby.Conclusion: You will cry. C. Hypothesis: Babies cry.Conclusion: You are a baby. D. none of the above

5. Example Write a Conditional in If-Then Form Write the statement in if-then form. Then identify the hypothesis and conclusion of the statement. A five-sided polygon is a pentagon. Answer: If a polygon has five sides, then it is a pentagon. Hypothesis: A polygon has five sides.Conclusion: It is a pentagon.

6. Example Which of the following is the correct if-then form of the given statement?An angle that measures 45° is an acute angle. A. If an angle is acute, then it measures less than 90°. B. If an angle is not obtuse, then it is acute. C. If an angle measures 45°, then it is an acute angle. D. If an angle is acute, then it measures 45°.

7. Example Truth Values of Conditionals Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample. If last month was February, then this month is March. True; March is the month that follows February.

8. Example Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample. The product of whole numbers is greater than or equal to 0. • True; 3 ● 5 = 15, 8● 2 = 16 • B. False; –3 ● 4 = –12

9. Converse • Switch the “if” and “then” • Think opposite, or CON-artist • If q, then p. Example: If today is Friday, then tomorrow is Saturday True Converse If tomorrow is Saturday, then today is Friday True Underline hypothesis once Underline conclusion twice

10. TOO • Think of your own “if-then” statement where the original statement is true, but the converse is false • Anyone want to share???

11. P: HYPOTHESIS Q: CONCLUSION • Recall: Statement If p, then q • Recall: Converse If q, then p • (con-artist—does a switch) • Inverse If not p, then not q • Add a word In---not • Contrapositive If not q, then not p • Weirdest word—so do both, add NOT and Switch

12. EXAMPLES: Give the Converse, Inverse and Contrapos. State Tor F If a parallelogram is a square, then it is a rectangle. (T) C: If a parallelogram is a rectangle, then it is a square. (F) I: If a parallelogram is not a square, then it is not a rectangle (F) C+: If a parallelogram is not a rectangle, then it is not a square (T)

13. RULE!!!!!!!!!!!!!! • Related conditionals • Aconditional statement and its contrapositive are logically equivalent. Either both are true or both are false. • The converse and the inverse are logically equivalent. Either both are true or both are false.

14. Homework! (write it down!!!!!!!!) • Pg.111 #19-51 odd(skip #41) 53-56, 58-61, 68 ALL • ON a Separate paper!!!!!!!!!!!